Paper 2016/462

Fully Homomorphic Encryption with Isotropic Elements

Masahiro Yagisawa

Abstract

In previous work I proposed a fully homomorphic encryption without bootstrapping which has the weak point in the enciphering function. In this paper I propose the fully homomorphic encryption scheme with non-zero isotropic octonions. I improve the previous scheme by adopting the non-zero isotropic octonions so that the “m and -m attack” is not useful because in proposed scheme many ciphertexts exist where the plaintext m is not zero and the norm is zero. The improved scheme is based on multivariate algebraic equations with high degree or too many variables while the almost all multivariate cryptosystems proposed until now are based on the quadratic equations avoiding the explosion of the coefficients. The improved scheme is against the Gröbner basis attack.

Note: In previous report 2015/474,2015/733 in Cryptology ePrint Archive, I proposed fully homomorphic encryption which has the weak point in the enciphering function and is not immune from “m and -m attack”. In this report I propose the improved scheme which overcomes the weak point.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Published elsewhere. Major revision. Masahiro, Y. (2015). Fully Homomorphic Encryption without bootstrapping which was published by LAP LAMBERT Academic Publishing, Saarbrücken/Germany
Keywords
fully homomorphic encryptionisotropic octonionmultivariate algebraic equationGröbner basis
Contact author(s)
tfkt8398yagi @ hb tp1 jp
History
2016-05-13: received
Short URL
https://ia.cr/2016/462
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2016/462,
      author = {Masahiro Yagisawa},
      title = {Fully Homomorphic Encryption with Isotropic Elements},
      howpublished = {Cryptology ePrint Archive, Paper 2016/462},
      year = {2016},
      note = {\url{https://eprint.iacr.org/2016/462}},
      url = {https://eprint.iacr.org/2016/462}
}
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